Statistics.Distribution

Types classes for probability distrubutions

Type classes

class Distribution d where

Type class common to all distributions. Only c.d.f. could be defined for both discrete and continous distributions.

Methods

cumulative :: d -> Double -> Double

Cumulative distribution function. The probability that a random variable X is less or equal than x, i.e. P(X≤x).

Instances

Distribution GeometricDistribution

Distribution ExponentialDistribution

Distribution NormalDistribution

Distribution BinomialDistribution

Distribution ChiSquared

Distribution GammaDistribution

Distribution HypergeometricDistribution

Distribution PoissonDistribution

class Distribution d => DiscreteDistr d where

Discrete probability distribution.

Methods

probability :: d -> Int -> Double

Probability of n-th outcome.

Instances

DiscreteDistr GeometricDistribution

DiscreteDistr BinomialDistribution

DiscreteDistr HypergeometricDistribution

DiscreteDistr PoissonDistribution

class Distribution d => ContDistr d where

Continuous probability distributuion

Methods

density :: d -> Double -> Double

Probability density function. Probability that random variable X lies in the infinitesimal interval [x,x+δx) equal to density(x)⋅δx

quantile :: d -> Double -> Double

Inverse of the cumulative distribution function. The value x for which P(X≤x) = p.

Instances

ContDistr ExponentialDistribution

ContDistr NormalDistribution

ContDistr ChiSquared

ContDistr GammaDistribution

class Distribution d => Mean d where

Type class for distributions with mean.

Methods

mean :: d -> Double

Instances

Mean GeometricDistribution

Mean ExponentialDistribution

Mean NormalDistribution

Mean BinomialDistribution

Mean ChiSquared

Mean GammaDistribution

Mean HypergeometricDistribution

Mean PoissonDistribution

class Mean d => Variance d where

Type class for distributions with variance.

Methods

variance :: d -> Double

Instances

Variance GeometricDistribution

Variance ExponentialDistribution

Variance NormalDistribution

Variance BinomialDistribution

Variance ChiSquared

Variance GammaDistribution

Variance HypergeometricDistribution

Variance PoissonDistribution

Helper functions

findRoot

Arguments

:: ContDistr d

=> d

Distribution

-> Double

Probability p

-> Double

Initial guess

-> Double

Lower bound on interval

-> Double

Upper bound on interval

-> Double

Approximate the value of X for which P(x>X)=p.

This method uses a combination of Newton-Raphson iteration and bisection with the given guess as a starting point. The upper and lower bounds specify the interval in which the probability distribution reaches the value p.

sumProbabilities :: DiscreteDistr d => d -> Int -> Int -> Double

Sum probabilities in inclusive interval.